Exercise 20.  Many texts give an alternative definition for  [Graphics:Images/ComplexFunExponentialModHome_gr_643.gif],  starting with (5-1) as the definition for  [Graphics:Images/ComplexFunExponentialModHome_gr_644.gif].  

20 (a).  Use the result  [Graphics:Images/ComplexFunExponentialModHome_gr_651.gif]  and the requirement  [Graphics:Images/ComplexFunExponentialModHome_gr_652.gif]  from condition (2) to show that  

                    [Graphics:Images/ComplexFunExponentialModHome_gr_653.gif],   and   [Graphics:Images/ComplexFunExponentialModHome_gr_654.gif],    for all   [Graphics:Images/ComplexFunExponentialModHome_gr_655.gif].

Solution 20 (a).

See text and/or instructor's solution manual.

Solution.   [Graphics:../Images/ComplexFunExponentialModHome_gr_656.gif]   implies   [Graphics:../Images/ComplexFunExponentialModHome_gr_657.gif],   

                    [Graphics:../Images/ComplexFunExponentialModHome_gr_658.gif],

and

                    [Graphics:../Images/ComplexFunExponentialModHome_gr_659.gif].

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This solution is complements of the authors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) 2008 John H. Mathews, Russell W. Howell